That is just a little idiosyncrasy that Photoshop has had for ages. It is confusing but technically justified. When the source of an image is the Camera Raw plugin, what opens in PS proper is a rasterized bitmap which at that moment exists only in memory because nothing has as yet been written to disc. Since the image hasn't been saved, it can't be identified as being in a particular format (psd, tif, jpg, etc.) so PS identifies it by its origin in the Raw file - in your case an ARW. When LrC and PS/ACR are parallel versions, the "Edit in ..." causes LrC to send across, not a link to a converted and saved tif (or whatever), but rather only data, the Raw data from the ARW + LrC's relevant catalog data. From that point the CR > PS datastream is the same as always and as usual the raster image carries the name of the Raw file. When, however, the two apps are not concurrent, LrC has to do the heavy lifting, process a conversion and write an image format to disc. Thus, when PS finally gets the goods it is just like opening any other saved file and the display tab bears the regular (RGB) format name.
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